The derivation of the DE SINR \( \bar{\gamma }_{g_{k},\mathrm {PGP}} \)  is obtained by following the approach in [1]} but with extension to imperfect CSI that brings considerable differences. Hence, taking into account for imperfect CSI, the proof consists of the derivation of the DEs of four parts: i) The power normalization term \( \Psi _{g} \) , ii) the desired signal power part \( \mathrm {DS}_{g_{k}} \) , iii) the self-group interference power part \( \mathrm {SGI}_{g_{k}} \) , and iv) the inter-group interference power part \( \mathrm {IGI}_{g_{k}} \) .
